Sharing a secret

[an41418@anon.penet.fi (wonderer)]

I posed a newbie question a while ago that resulted
in a great summary of how detecting double spending in
Chaum's paper works. Not only do I understand it now, but
I'vee seen that explanation distributed on other mailing
lists at my institution by others who read cypherpunks.

Here's another question that most of you know the answer
to, but the rest of us would greatly benefit from a simple,
detailed expanation. In fact, if we get some more great
summaries that are simplified the way the digital cash
solution was simplified, we could produce an excellent
FAQ. I am keeping these with plans to make such a document
available (though a FAQ is probably not the form it will 
take).

I know that there is a way to have a key, K, divided into
n parts such that any i of them are needed to recunstruct
K. The property holds that no i-1 parts are sufficient,
and ANY i parts will do. How does this work exactly? Is
it really the case that no i-1 parts give information?
Is there a way to cheat? 

A good explanation would be great.

BTW, many of you are exposing your anonymous ID's to me
when you reply to my posts. If you are concerned with 
keeping your anonymous identity, you have to be careful.

One more thing - I posted something yesterday that took
about 12 hours from the time I posted it to Finland until
it appeared on Cypherpunks. I think this is because Julf's
remailer is a bit overloaded. Due to this, my post
(about burning instead of shredding) arrived after 3
other people had posted the same idea. Please pardon
such posts. The delay would make it appear that one
is not following the list, but I can think of no way
around it.

Wonderer
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